Intersection of Sets
Pronunciation: /ˌɪn tərˈsɛk ʃən/ ?
|Figure 1: Intersection. Click on the image to see a representation of A ∩ B.||
An intersection of two or more
is a set containing the members that are in all of the sets. This is spoken, "Set
C is the intersection of sets
A and B."
This is written, C = A ∩ B.
Properties of Intersection of Sets
|Commutative||A ∩ B = B ∩ A||The intersection of sets is commutative|
|Associative||(D ∩ E) ∩ F = D ∩ (E ∩ F)||The intersection of sets is associative|
|Distributive||(D ∩ E) ∪ F = (D ∪ F) ∩ (E ∪ F)|
(D ∪ E) ∩ F = (D ∩ F) ∪ (E ∩ F)
|The intersection and union of sets are distributive|
|Table 1: Properties of the intersection of two sets.|
- intersection. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2010-02-23). http://www.merriam-webster.com/dictionary/intersection.
- Von Neumann, John and Morgenstern, Oskar. Theory Of Games And Economic Behavior, 3rd edition, pg 63. Princeton University Press, 1953. (Accessed: 2010-02-23). http://www.archive.org/stream/theoryofgamesand030098mbp#page/n84/mode/1up.
- Goldrei, D.C.. Classic Set Theory: For Guided Independent Study, pg 4. Chapman & Hall Mathematics, July 1, 1996.
- Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pg 4. Thomson, Brooks/Cole, 2005.
- McAdams, David. Sets. lifeisastoryproblem.com. Life is a Story Problem LLC. 2009-03-12. http://www.lifeisastoryproblem.com/algebra/sets.html.
- McAdams, David. Set. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-12-15. http://www.allmathwords.org/article.aspx?lang=en&id=Set.
Cite this article as:
Intersection of Sets. 2010-02-23. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/intersection.html.
2010-02-23: Added "References" (McAdams, David.
2008-06-07: Corrected spelling (McAdams, David.
2008-03-28: Added properties (McAdams, David.
2007-08-01: Initial version (McAdams, David.